A method has been developed to measure the spin-lattice and spin-spin relaxation times of the various components of a multi-component spectrum. By Fourier transforming the free induction decay after the inversion recovery or spin echo pulse sequences, the different frequency components can be resolved and their individual relaxation times can be measured. This method has great advantages over the conventional method of analysis for multiple component decays which are very common in chemical and biological system. Based on this method, many interesting studies can now be done with NMR. The details of this method are presented with a comparison between our method and the conventional method and results and discussion of some applications.